The 29-year-old started his career in the youth set-up at Portsmouth before signing for West Bromwich Albion at the age of 17.
The winger joined Scottish side Falkirk in 2010, where he made thirty-seven appearances before re-joining Portsmouth in 2012.
In January 2013 he joined Colchester United where he became the 600th player to play for the club in the Football League.
In June 2013, Compton signed for Hartlepool United where he played fifty-five times, scoring 4 goals.
He moved south to join Yeovil Town in the summer of 2015, making twenty appearances, and then onto Newport County a year later.
Last season he turned out for Chippenham`s neighbours Bath City, winning the `golden boot` and the goal of the season award.
Chippenham manager Mark Collier told the club`s Pitchero website: "Jack is a great signing for the club, he will add a real quality to the squad, he was very much sought after following his goals and assists last season".